x=(4+2root3)find (x-2÷root x)
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Answer:
5 + √3
Solution:
Given : x = 4 + 2√3
To find : x - 2/√x = ?
Firstly ,
Let's find the value of √x .
We have ;
=> x = 4 + 2√3
=> x = 3 + 1 + 2√3
=> x = 3 + 2√3 + 1
=> x = (√3)² + 2•√3•1 + (1)²
=> x = (√3 + 1)²
=> √x = √3 + 1
Now,
Let's find the value of 2/√x .
We have ;
=> √x = √3 + 1
=> 1/√x = 1 / (√3 + 1)
=> 1/√x = (√3 - 1) / (√3 + 1)(√3 - 1)
=> 1/√x = (√3 - 1) / { (√3)² - 1² }
=> 1/√x = (√3 - 1) / (3 - 1)
=> 1/√x = (√3 - 1) / 2
=> 2/√x = √3 - 1
Now,
x - 2/√x = (4 + 2√3) - (√3 - 1)
= 4 + 2√3 - √3 + 1
= 5 + √3
Hence,
The required answer is :
5 + √3
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